Random Matrices and the Glasgow Method

Abstract

A simple non-Hermitean random matrix (RM) model is used to study the Glasgow method of finite-density lattice QCD. The zeros of the RM partition function are evaluated through an averaging procedure, involving the zeros of the RM 'propagator matrix' in the complex chemical-potential plane. The nature of the uncertainty affecting the results is similar to that produced by rounding errors in computing the known analytic result. This similarity is exploited to give quantitative estimates on the relationship between the size of the matrix and the number of configurations needed to achieve a given precision. For the quenched ensemble considered here, the relationship is exponential.